rlq
Kaushik Narasimhan
7/6/2020
RLQ analysis
Prepare data
When preparing palm traits for analysis, I had to remove several variables that contained NAs for our palm species. Also, I removed the descriptive traits about the fruit, and the variable “FruitShape” because it has blank values.
Run RLQ analysis and plot data
To successfully run this, I had to remove Habitat type from our environmental variables. The problem might be the naming convention. Sarah, can you make three letter codes for these?
That’s unreadable, plotting as seperate.
Summary of RLQ analysis. How to interpret this?
## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = acpR.aravo, dudiL = afcL.aravo, dudiQ = acpQ.aravo,
## scannf = FALSE)
##
## Total inertia: 0.657
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.300155 0.228303 0.083533 0.041707 0.001744
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 45.6877 34.7508 12.7148 6.3484 0.2654
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 45.69 80.44 93.15 99.50 99.77
##
## (Only 5 dimensions (out of 9) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.3001551 0.5478641 1.034229 1.481707 0.3575146
## 2 0.2283026 0.4778102 1.084627 2.004471 0.2197734
##
## Inertia & coinertia R (acpR.aravo):
## inertia max ratio
## 1 1.069629 1.755539 0.6092881
## 12 2.246045 3.085130 0.7280229
##
## Inertia & coinertia Q (acpQ.aravo):
## inertia max ratio
## 1 2.195457 5.095305 0.4308784
## 12 6.213361 7.950625 0.7814933
##
## Correlation L (afcL.aravo):
## corr max ratio
## 1 0.3575146 0.9327084 0.3833080
## 2 0.2197734 0.8335977 0.2636445Fourth-corner analysis
From tutorial: “Fourth-corner analysis can be used to test the associations between individual traits and environmental variables. To obtain a test with a correct type I error, results of model 2 (permutation of sites, i.e. rows) and 4 (permutation of species, i.e. columns) should be combined.”
nrepet <- 999
four.comb.aravo <- fourthcorner(p_env[,-10], p_species,
p_traits, modeltype = 6, p.adjust.method.G = "none",
p.adjust.method.D = "none", nrepet = nrepet)Plotting the data: “Blue cells correspond to negative significant relationships while red cells correspond to positive significant relationships (this can be modified using the argument col).”
I used the D2 option when plotting, but others exist: stat=“D2”: the association is measured between the quantitative variable and each category separately. A correlation coefficient is used to indicate the strength of the association between the given category and the small or large values of the quantitative variable. stat=“G”: the association between the quantitative variable and the whole categorical variable is measured by a global statistic (F). stat=“D”: the association is estimated between the quantitative variable and each category separately by a measure of the within-group homogeneity. The strength of the association is indicated by the dispersion of the values of the quantitative variable for a given category.
To replot the data for multiple comparisons: “Now, we adjust p-values for multiple comparisons (here we used the fdr method using the p.adjust.4thcorner function).”
Combine both approaches
“First, a multivariate test can be applied to evaluate the global significance of the traits-environment relationships. This test is based on the total inertia of the RLQ analysis”
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.aravo, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 0.6569709 -0.1346780 greater 0.507
## 2 Model 4 0.6569709 -0.9536772 greater 0.829
The total inertia of RLQ analysis is equal to the SRLQ multivariate statistic defined in Dray and Legendre (2008). This statistic is returned by the fourthcorner2 function:
Srlq <- fourthcorner2(p_env[,-10], p_species, p_traits,
modeltype = 6, p.adjust.method.G = "fdr", nrepet = nrepet)
Srlq$trRLQ## Monte-Carlo test
## Call: fourthcorner2(tabR = p_env[, -10], tabL = p_species, tabQ = p_traits,
## modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: -8990.343
##
## Based on 999 replicates
## Simulated p-value: 0.822
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## -9.206018e-01 -8.990088e+03 7.649906e-02“Both approaches can be combined if RLQ scores are used to represent traits and environmental variables on a biplot. Then, significant associations revealed by the fourthcorner approach can be represented using segments (blue lines for negative associations, red lines for positive associations, see the argument col). Only traits and environmental variables that have at least one significant association are represented. Here, we apply this method using adjusted pvalues for multiple comparisons and a significant level α = 0.05.”
“Another approach is provided by the fourthcorner.rlq function and consists in testing directly the links between RLQ axes and traits (typetest=”Q.axes“) or environmental variables (typetest=”R.axes“).”
RLQ axes and traits
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.aravo, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.96134310 2.20116058 less
## 2 AxcR2 / Climb.0 Homog. 0.89121986 -0.53679743 less
## 3 AxcR1 / Climb.1 Homog. 0.03686797 -0.24848563 less
## 4 AxcR2 / Climb.1 Homog. 0.10785496 1.78642185 less
## 5 AxcR1 / Acaul.0 Homog. 1.00000000 <NA> less
## 6 AxcR2 / Acaul.0 Homog. 1.00000000 <NA> less
## 7 AxcR1 / Erect.0 Homog. 0.03686797 -0.24848563 less
## 8 AxcR2 / Erect.0 Homog. 0.10785496 1.78642185 less
## 9 AxcR1 / Erect.1 Homog. 0.96134310 2.20116058 less
## 10 AxcR2 / Erect.1 Homog. 0.89121986 -0.53679743 less
## 11 AxcR1 / StemS.0 Homog. 0.03698011 -0.82249690 less
## 12 AxcR2 / StemS.0 Homog. 0.10811460 1.69818917 less
## 13 AxcR1 / StemS.1 Homog. 0.48052421 -0.47715061 less
## 14 AxcR2 / StemS.1 Homog. 0.59926258 0.29260277 less
## 15 AxcR1 / StemS.2 Homog. 0.41908006 3.49481660 less
## 16 AxcR2 / StemS.2 Homog. 0.27599200 0.82078570 less
## 17 AxcR1 / StemA.0 Homog. 0.76595294 1.53669110 less
## 18 AxcR2 / StemA.0 Homog. 0.63295693 -1.43746503 less
## 19 AxcR1 / StemA.1 Homog. 0.20361638 0.26186245 less
## 20 AxcR2 / StemA.1 Homog. 0.32299828 0.83189141 less
## 21 AxcR1 / Leave.0 Homog. 0.72348658 2.13924819 less
## 22 AxcR2 / Leave.0 Homog. 0.52504761 -1.56755644 less
## 23 AxcR1 / Leave.1 Homog. 0.24149577 0.02111477 less
## 24 AxcR2 / Leave.1 Homog. 0.44244854 1.66729070 less
## 25 AxcR1 / MaxStemHeight_m r 0.09149172 0.68994881 two-sided
## 26 AxcR2 / MaxStemHeight_m r -0.14448147 -1.18998713 two-sided
## 27 AxcR1 / MaxStemDia_cm r 0.08749172 0.67358979 two-sided
## 28 AxcR2 / MaxStemDia_cm r -0.12934431 -1.06921687 two-sided
## 29 AxcR1 / Under.canopy Homog. 0.97761339 1.77069366 less
## 30 AxcR2 / Under.canopy Homog. 0.96901013 0.58548969 less
## 31 AxcR1 / Under.understorey Homog. 0.02065195 -0.45299627 less
## 32 AxcR2 / Under.understorey Homog. 0.03098774 -0.29627554 less
## 33 AxcR1 / AverageFruitLength_cm r 0.24503760 1.89727497 two-sided
## 34 AxcR2 / AverageFruitLength_cm r -0.12292261 -0.96520838 two-sided
## 35 AxcR1 / Fruit.large Homog. 0.42030052 2.10914139 less
## 36 AxcR2 / Fruit.large Homog. 0.51860246 2.78553943 less
## 37 AxcR1 / Fruit.small Homog. 0.55423824 2.73768704 less
## 38 AxcR2 / Fruit.small Homog. 0.46746559 1.25826119 less
## 39 AxcR1 / Consp.conspicuous Homog. 0.28302363 -1.35476992 less
## 40 AxcR2 / Consp.conspicuous Homog. 0.49950186 1.79562903 less
## 41 AxcR1 / Consp.cryptic Homog. 0.67206694 1.88678666 less
## 42 AxcR2 / Consp.cryptic Homog. 0.46811068 -0.15736019 less
## Pvalue Pvalue.adj
## 1 0.996 1
## 2 0.261 0.8150625
## 3 0.61 0.8150625
## 4 0.946 1
## 5 1 1
## 6 1 1
## 7 0.61 0.8150625
## 8 0.946 1
## 9 0.996 1
## 10 0.261 0.8150625
## 11 0.241 0.8150625
## 12 0.942 1
## 13 0.308 0.8150625
## 14 0.584 0.8150625
## 15 0.993 1
## 16 0.833 1
## 17 0.929 1
## 18 0.099 0.693
## 19 0.594 0.8150625
## 20 0.811 1
## 21 0.967 1
## 22 0.07 0.6216
## 23 0.538 0.8150625
## 24 0.966 1
## 25 0.527 0.8150625
## 26 0.264 0.8150625
## 27 0.524 0.8150625
## 28 0.296 0.8150625
## 29 0.973 1
## 30 0.713 1
## 31 0.504 0.8150625
## 32 0.571 0.8150625
## 33 0.046 0.6216
## 34 0.366 0.8150625
## 35 0.973 1
## 36 0.993 1
## 37 0.988 1
## 38 0.911 1
## 39 0.074 0.6216
## 40 0.976 1
## 41 0.944 1
## 42 0.429 0.8150625
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1RLQ axes and environmental variables
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.aravo, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue
## 1 Canopy.Cover / AxcQ1 r -0.012420893 -0.08504096 two-sided 0.891
## 2 Understory.Density / AxcQ1 r -0.029892325 -0.28535590 two-sided 0.784
## 3 Leaf.Litter / AxcQ1 r 0.083803687 0.83347452 two-sided 0.432
## 4 Soil.Moisture / AxcQ1 r 0.122365689 1.10765079 two-sided 0.265
## 5 Cec / AxcQ1 r 0.046971395 1.03900906 two-sided 0.333
## 6 T50 / AxcQ1 r 0.009956983 0.17613818 two-sided 0.897
## 7 T10 / AxcQ1 r 0.304644385 1.82411195 two-sided 0.079
## 8 Canopy.Height / AxcQ1 r -0.124070105 -1.03016040 two-sided 0.331
## 9 Elevation / AxcQ1 r 0.056259879 0.43232450 two-sided 0.687
## 10 Canopy.Cover / AxcQ2 r 0.014571724 0.12684783 two-sided 0.846
## 11 Understory.Density / AxcQ2 r -0.114617370 -1.15933364 two-sided 0.27
## 12 Leaf.Litter / AxcQ2 r 0.049781194 0.49259572 two-sided 0.636
## 13 Soil.Moisture / AxcQ2 r -0.068450849 -0.84961406 two-sided 0.419
## 14 Cec / AxcQ2 r 0.027732905 0.71951008 two-sided 0.499
## 15 T50 / AxcQ2 r 0.098808237 1.14865071 two-sided 0.219
## 16 T10 / AxcQ2 r -0.062682617 -0.36973774 two-sided 0.699
## 17 Canopy.Height / AxcQ2 r -0.090071839 -0.81666971 two-sided 0.48
## 18 Elevation / AxcQ2 r 0.117191890 0.95719518 two-sided 0.367
## Pvalue.adj
## 1 0.891
## 2 0.882
## 3 0.816545454545455
## 4 0.777857142857143
## 5 0.816545454545455
## 6 0.897
## 7 0.708
## 8 0.816545454545455
## 9 0.834352941176471
## 10 0.891
## 11 0.777857142857143
## 12 0.834352941176471
## 13 0.816545454545455
## 14 0.816545454545455
## 15 0.777857142857143
## 16 0.834352941176471
## 17 0.816545454545455
## 18 0.816545454545455
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Results can be represented using a table with colors indicating significance :
Significance with axes can also be reported on the factorial map of RLQ analysis. Here, significant associations with the first axis are represented in blue, with the second axis in orange, with both axes in green (variables with no significant association are in black)
RUN 2 RLQ/4th corner: Splitting all lifestage and points with some forest cover
Run RLQ/ FQ analysis for all lifestage types
That’s unreadable, plotting as separate.
## [1] "RLQ for juveniles"
## [1] "RLQ for adults"
Summary of RLQ analysis. How to interpret this?
## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Rjuv, dudiL = Ljuv, dudiQ = Qjuv, scannf = FALSE)
##
## Total inertia: 1.429
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.746537 0.500895 0.121014 0.054025 0.003262
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 52.2481 35.0563 8.4695 3.7811 0.2283
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 52.25 87.30 95.77 99.55 99.78
##
## (Only 5 dimensions (out of 9) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.7465371 0.8640238 1.170836 1.785317 0.4133466
## 2 0.5008948 0.7077392 1.244773 1.691688 0.3360957
##
## Inertia & coinertia R (Rjuv):
## inertia max ratio
## 1 1.370856 1.858611 0.7375703
## 12 2.920316 3.464436 0.8429412
##
## Inertia & coinertia Q (Qjuv):
## inertia max ratio
## 1 3.187357 5.160919 0.6175949
## 12 6.049164 7.993775 0.7567344
##
## Correlation L (Ljuv):
## corr max ratio
## 1 0.4133466 0.9448971 0.4374514
## 2 0.3360957 0.9087471 0.3698452## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Radu, dudiL = Ladu, dudiQ = Qadu, scannf = FALSE)
##
## Total inertia: 1.04
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.564979 0.338546 0.115397 0.015354 0.003838
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 54.314 32.546 11.094 1.476 0.369
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 54.31 86.86 97.95 99.43 99.80
##
## (Only 5 dimensions (out of 10) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.5649794 0.7516511 1.317944 1.702729 0.3349451
## 2 0.3385457 0.5818468 1.128801 2.171484 0.2373747
##
## Inertia & coinertia R (Radu):
## inertia max ratio
## 1 1.736977 2.095715 0.8288231
## 12 3.011170 3.680365 0.8181714
##
## Inertia & coinertia Q (Qadu):
## inertia max ratio
## 1 2.899287 4.937157 0.5872382
## 12 7.614631 7.890549 0.9650318
##
## Correlation L (Ladu):
## corr max ratio
## 1 0.3349451 1.0000000 0.3349451
## 2 0.2373747 0.9128287 0.2600430Fourth-corner analysis
## [1] "FQ for juveniles"
## [1] "FQ for adults"
With adjusted p-values
## [1] "FQ for Juveniles"## [1] "FQ for Adults"
Combine both approaches
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 1.442008 0.2686947 greater 0.367
## 2 Model 4 1.442008 -0.3683070 greater 0.599
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 1.035941 15.3419891 greater 0.001
## 2 Model 4 1.035941 -0.1279593 greater 0.503
The total inertia of RLQ analysis is equal to the SRLQ multivariate statistic defined in Dray and Legendre (2008). This statistic is returned by the fourthcorner2 function:
## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envFORCOVER, tabL = p_speciesJUV, tabQ = p_traits[,
## -2], modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: 1.442008
##
## Based on 858 replicates
## Simulated p-value: 0.5518044
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## 3.893864e-01 -1.853161e+03 2.268507e+07## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envFORCOVER, tabL = p_speciesADU, tabQ = p_traits[,
## -2], modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: 1.035941
##
## Based on 999 replicates
## Simulated p-value: 0.487
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## 3.627491e-01 -1.798911e+03 2.462105e+07## [1] "juvenile"
## [1] "adult"
“Another approach is provided by the fourthcorner.rlq function and consists in testing directly the links between RLQ axes and traits (typetest=”Q.axes“) or environmental variables (typetest=”R.axes“).”
RLQ axes and traits
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.943613890 1.38352846 less
## 2 AxcR2 / Climb.0 Homog. 0.909518009 -0.29764535 less
## 3 AxcR1 / Climb.1 Homog. 0.053447423 -0.05495846 less
## 4 AxcR2 / Climb.1 Homog. 0.084371434 0.16475841 less
## 5 AxcR1 / Erect.0 Homog. 0.053447423 -0.05495846 less
## 6 AxcR2 / Erect.0 Homog. 0.084371434 0.16475841 less
## 7 AxcR1 / Erect.1 Homog. 0.943613890 1.38352846 less
## 8 AxcR2 / Erect.1 Homog. 0.909518009 -0.29764535 less
## 9 AxcR1 / StemS.0 Homog. 0.053447423 -0.49833525 less
## 10 AxcR2 / StemS.0 Homog. 0.084371434 0.16475841 less
## 11 AxcR1 / StemS.1 Homog. 0.428025862 -0.73020926 less
## 12 AxcR2 / StemS.1 Homog. 0.521201486 -0.21515194 less
## 13 AxcR1 / StemS.2 Homog. 0.347338026 2.27271748 less
## 14 AxcR2 / StemS.2 Homog. 0.386202949 2.87861842 less
## 15 AxcR1 / StemA.0 Homog. 0.826344445 2.38518552 less
## 16 AxcR2 / StemA.0 Homog. 0.576845878 -1.70242052 less
## 17 AxcR1 / StemA.1 Homog. 0.170876549 0.03530479 less
## 18 AxcR2 / StemA.1 Homog. 0.292200392 0.78366931 less
## 19 AxcR1 / Leave.0 Homog. 0.768813593 2.58506552 less
## 20 AxcR2 / Leave.0 Homog. 0.492148977 -1.63730148 less
## 21 AxcR1 / Leave.1 Homog. 0.224844454 -0.02492680 less
## 22 AxcR2 / Leave.1 Homog. 0.424884198 1.62034436 less
## 23 AxcR1 / MaxStemHeight_m r -0.208407212 -1.35478741 two-sided
## 24 AxcR2 / MaxStemHeight_m r -0.078947746 -0.64599103 two-sided
## 25 AxcR1 / MaxStemDia_cm r -0.209187895 -1.35875846 two-sided
## 26 AxcR2 / MaxStemDia_cm r -0.054305894 -0.49393222 two-sided
## 27 AxcR1 / Under.canopy Homog. 0.981347340 0.91793232 less
## 28 AxcR2 / Under.canopy Homog. 0.981120201 0.87789559 less
## 29 AxcR1 / Under.understorey Homog. 0.017227001 -0.55517715 less
## 30 AxcR2 / Under.understorey Homog. 0.018790061 -0.54651300 less
## 31 AxcR1 / AverageFruitLength_cm r -0.412507031 -2.73863068 two-sided
## 32 AxcR2 / AverageFruitLength_cm r -0.007459463 -0.08050279 two-sided
## 33 AxcR1 / Fruit.large Homog. 0.381757814 1.54708263 less
## 34 AxcR2 / Fruit.large Homog. 0.473864901 2.21056477 less
## 35 AxcR1 / Fruit.small Homog. 0.520672457 2.44145746 less
## 36 AxcR2 / Fruit.small Homog. 0.525158287 2.34585118 less
## 37 AxcR1 / Consp.conspicuous Homog. 0.257598643 -1.27517886 less
## 38 AxcR2 / Consp.conspicuous Homog. 0.462805149 1.52340090 less
## 39 AxcR1 / Consp.cryptic Homog. 0.731937157 2.46836745 less
## 40 AxcR2 / Consp.cryptic Homog. 0.452042297 -0.22024949 less
## Pvalue Pvalue.adj
## 1 0.943 0.996
## 2 0.249 0.845882352941176
## 3 0.640229885057471 0.845882352941176
## 4 0.608 0.996
## 5 0.640229885057471 0.845882352941176
## 6 0.608 0.996
## 7 0.943 0.996
## 8 0.249 0.845882352941176
## 9 0.457661290322581 0.845882352941176
## 10 0.608 0.996
## 11 0.268 0.845882352941176
## 12 0.432 0.845882352941176
## 13 0.962 0.996
## 14 0.984 0.996
## 15 0.992 0.996
## 16 0.057 0.528
## 17 0.559 0.845882352941176
## 18 0.785 0.996
## 19 0.996 0.996
## 20 0.066 0.528
## 21 0.531 0.845882352941176
## 22 0.961 0.996
## 23 0.197 0.845882352941176
## 24 0.563 0.996
## 25 0.181 0.845882352941176
## 26 0.664 0.996
## 27 0.833 0.996
## 28 0.8 0.996
## 29 0.484814398200225 0.845882352941176
## 30 0.565804274465692 0.845882352941176
## 31 0.001 0.04 *
## 32 0.947 0.996
## 33 0.934 0.957948717948718
## 34 0.979 0.979
## 35 0.981 0.996
## 36 0.973 0.996
## 37 0.118 0.786666666666667
## 38 0.955 0.996
## 39 0.995 0.996
## 40 0.43 0.845882352941176
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.83426767 -1.24218503 less
## 2 AxcR2 / Climb.0 Homog. 0.95099413 0.87198368 less
## 3 AxcR1 / Climb.1 Homog. 0.07511623 1.20481129 less
## 4 AxcR2 / Climb.1 Homog. 0.04845745 -0.10705234 less
## 5 AxcR1 / Erect.0 Homog. 0.07511623 1.20481129 less
## 6 AxcR2 / Erect.0 Homog. 0.04845745 -0.10705234 less
## 7 AxcR1 / Erect.1 Homog. 0.83426767 -1.24218503 less
## 8 AxcR2 / Erect.1 Homog. 0.95099413 0.87198368 less
## 9 AxcR1 / StemS.0 Homog. 0.09973008 2.81986579 less
## 10 AxcR2 / StemS.0 Homog. 0.05482648 -0.54811255 less
## 11 AxcR1 / StemS.1 Homog. 0.64768119 0.62599905 less
## 12 AxcR2 / StemS.1 Homog. 0.71039950 0.83245462 less
## 13 AxcR1 / StemS.2 Homog. 0.15422535 -0.96229547 less
## 14 AxcR2 / StemS.2 Homog. 0.20727085 -0.54834780 less
## 15 AxcR1 / StemA.0 Homog. 0.63755477 1.50219243 less
## 16 AxcR2 / StemA.0 Homog. 0.62430580 0.69773950 less
## 17 AxcR1 / StemA.1 Homog. 0.33541957 1.41660183 less
## 18 AxcR2 / StemA.1 Homog. 0.36632872 1.46725454 less
## 19 AxcR1 / Leave.0 Homog. 0.48818798 -1.92147038 less
## 20 AxcR2 / Leave.0 Homog. 0.57383859 1.10112628 less
## 21 AxcR1 / Leave.1 Homog. 0.51160198 2.25099033 less
## 22 AxcR2 / Leave.1 Homog. 0.41483194 1.19671885 less
## 23 AxcR1 / MaxStemHeight_m r -0.05356163 -0.29065001 two-sided
## 24 AxcR2 / MaxStemHeight_m r 0.25025122 1.87017083 two-sided
## 25 AxcR1 / MaxStemDia_cm r 0.07037235 0.50151065 two-sided
## 26 AxcR2 / MaxStemDia_cm r 0.24386735 1.88078829 two-sided
## 27 AxcR1 / Under.canopy Homog. 0.93589281 0.18237934 less
## 28 AxcR2 / Under.canopy Homog. 0.94840727 1.04665115 less
## 29 AxcR1 / Under.understorey Homog. 0.06357424 0.21559385 less
## 30 AxcR2 / Under.understorey Homog. 0.04964550 -0.04992555 less
## 31 AxcR1 / AverageFruitLength_cm r 0.02508289 0.20088746 two-sided
## 32 AxcR2 / AverageFruitLength_cm r 0.15744770 1.18935170 two-sided
## 33 AxcR1 / Fruit.large Homog. 0.45555129 2.44743065 less
## 34 AxcR2 / Fruit.large Homog. 0.55644465 2.86621912 less
## 35 AxcR1 / Fruit.small Homog. 0.53904796 3.44626257 less
## 36 AxcR2 / Fruit.small Homog. 0.40570765 -1.51656550 less
## 37 AxcR1 / Consp.conspicuous Homog. 0.57936912 2.11601780 less
## 38 AxcR2 / Consp.conspicuous Homog. 0.50416577 0.03958443 less
## 39 AxcR1 / Consp.cryptic Homog. 0.42033419 -0.41412270 less
## 40 AxcR2 / Consp.cryptic Homog. 0.47615401 -0.05341246 less
## Pvalue Pvalue.adj
## 1 0.07 0.4
## 2 0.817 0.999
## 3 0.88 0.999
## 4 0.650627615062761 0.968484848484849
## 5 0.88 0.999
## 6 0.650627615062761 0.968484848484849
## 7 0.07 0.4
## 8 0.817 0.999
## 9 0.997 0.999
## 10 0.402 0.861052631578947
## 11 0.709 0.968484848484849
## 12 0.804 0.999
## 13 0.2 0.727272727272727
## 14 0.35 0.861052631578947
## 15 0.938 0.999
## 16 0.763 0.999
## 17 0.897 0.96972972972973
## 18 0.877 0.96972972972973
## 19 0.034 0.4
## 20 0.867 0.999
## 21 0.985 0.999
## 22 0.846 0.96972972972973
## 23 0.799 0.968484848484849
## 24 0.049 0.4
## 25 0.646 0.968484848484849
## 26 0.052 0.4
## 27 0.557 0.912307692307692
## 28 0.844 0.999
## 29 0.667731629392971 0.968484848484849
## 30 0.667731629392971 0.968484848484849
## 31 0.866 0.96972972972973
## 32 0.261 0.861052631578947
## 33 0.992 0.999
## 34 0.999 0.999
## 35 0.999 0.999
## 36 0.063 0.21
## 37 0.978 0.999
## 38 0.498 0.948571428571429
## 39 0.358 0.861052631578947
## 40 0.491 0.948571428571429
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1RLQ axes and environmental variables
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 Canopy.Cover / AxcQ1 r -0.011478310 -0.09435422 two-sided 0.91 0.953333333333333
## 2 Understory.Density / AxcQ1 r -0.043904212 -0.26121892 two-sided 0.804 0.9273
## 3 Leaf.Litter / AxcQ1 r -0.005484529 -0.02763386 two-sided 0.981 0.981
## 4 Soil.Moisture / AxcQ1 r -0.225084984 -1.63397166 two-sided 0.12 0.528
## 5 Cec / AxcQ1 r -0.023971630 -0.16454271 two-sided 0.725 0.9273
## 6 T50 / AxcQ1 r 0.044249272 0.59011481 two-sided 0.614 0.898333333333333
## 7 T10 / AxcQ1 r -0.325127892 -1.54553960 two-sided 0.129 0.520666666666667
## 8 Canopy.Height / AxcQ1 r 0.092030583 0.62102573 two-sided 0.591 0.898333333333333
## 9 Elevation / AxcQ1 r 0.070324854 0.42198134 two-sided 0.71 0.898333333333333
## 10 Habit.Primary / AxcQ1 Homog. 0.331681420 -1.73563916 less 0.069 0.3795
## 11 Habit.Secondary / AxcQ1 Homog. 0.599381420 1.47891320 less 0.912 0.953
## 12 Canopy.Cover / AxcQ2 r -0.097263882 -1.26138728 two-sided 0.222 0.682
## 13 Understory.Density / AxcQ2 r -0.200252450 -1.67024964 two-sided 0.09 0.495
## 14 Leaf.Litter / AxcQ2 r 0.158914017 1.23240498 two-sided 0.251 0.682
## 15 Soil.Moisture / AxcQ2 r -0.075420075 -0.66916283 two-sided 0.54 0.898333333333333
## 16 Cec / AxcQ2 r 0.054906583 0.90105574 two-sided 0.394 0.796
## 17 T50 / AxcQ2 r 0.158470974 1.47641432 two-sided 0.17 0.534285714285714
## 18 T10 / AxcQ2 r 0.112190989 0.56034534 two-sided 0.591 0.898333333333333
## 19 Canopy.Height / AxcQ2 r -0.123081690 -0.94914207 two-sided 0.398 0.796
## 20 Elevation / AxcQ2 r 0.223865723 1.55322575 two-sided 0.142 0.520666666666667
## 21 Habit.Primary / AxcQ2 Homog. 0.552321876 1.02953064 less 0.843 0.9273
## 22 Habit.Secondary / AxcQ2 Homog. 0.447676330 -0.57625112 less 0.279 0.682
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 Canopy.Cover / AxcQ1 r -0.036559173 -0.8291895 two-sided 0.449 0.682
## 2 Understory.Density / AxcQ1 r -0.191817215 -2.2067015 two-sided 0.045 0.396
## 3 Leaf.Litter / AxcQ1 r 0.065828199 0.7223843 two-sided 0.527 0.682
## 4 Soil.Moisture / AxcQ1 r 0.195438294 1.9825725 two-sided 0.073 0.4015
## 5 Cec / AxcQ1 r 0.049119486 1.0689861 two-sided 0.323 0.619666666666667
## 6 T50 / AxcQ1 r -0.069148216 -1.7669571 two-sided 0.054 0.396
## 7 T10 / AxcQ1 r -0.094793506 -0.9921533 two-sided 0.335 0.619666666666667
## 8 Canopy.Height / AxcQ1 r 0.111040051 0.8764882 two-sided 0.333 0.619666666666667
## 9 Elevation / AxcQ1 r -0.282626507 -2.0599475 two-sided 0.041 0.396
## 10 Habit.Primary / AxcQ1 Homog. 0.629292241 4.4138312 less 1 1
## 11 Habit.Secondary / AxcQ1 Homog. 0.370594752 0.1728109 less 0.506 0.682
## 12 Canopy.Cover / AxcQ2 r -0.050123436 -1.2979342 two-sided 0.21 0.619666666666667
## 13 Understory.Density / AxcQ2 r -0.025867777 -0.3116514 two-sided 0.759 0.875809523809524
## 14 Leaf.Litter / AxcQ2 r 0.117444694 1.3798924 two-sided 0.182 0.619666666666667
## 15 Soil.Moisture / AxcQ2 r -0.077549281 -0.7294831 two-sided 0.492 0.682
## 16 Cec / AxcQ2 r 0.004084052 0.1301069 two-sided 0.905 0.9955
## 17 T50 / AxcQ2 r -0.009674346 -0.2513624 two-sided 0.82 0.949473684210526
## 18 T10 / AxcQ2 r 0.124474996 1.1152124 two-sided 0.338 0.619666666666667
## 19 Canopy.Height / AxcQ2 r 0.179515612 1.4784698 two-sided 0.149 0.619666666666667
## 20 Elevation / AxcQ2 r 0.030718449 0.2160426 two-sided 0.833 0.875809523809524
## 21 Habit.Primary / AxcQ2 Homog. 0.685658320 7.0650127 less 1 1
## 22 Habit.Secondary / AxcQ2 Homog. 0.313497605 -0.7161224 less 0.238 0.619666666666667
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Results can be represented using a table with colors indicating significance :
## [1] "juveniles"
## [1] "adults"
Significance with axes can also be reported on the factorial map of RLQ analysis. Here, significant associations with the first axis are represented in blue, with the second axis in orange, with both axes in green (variables with no significant association are in black)
## [1] "juveniles"
## [1] "adults"
RUN 3 RLQ/4th corner : Sarah data with endemism, distance to edge
First,Checking to see which environmental variables may be removed. Next, adding “endemism” as a trait and distance to edge as an environmental variable. Also, removing acualescence as a trait because it is 0 for all species
Run RLQ/ FQ analysis for all lifestage types with aforementioned additions and subtractions
That’s unreadable, plotting as separate.
## [1] "RLQ for juveniles"
## [1] "RLQ for adults"
Summary of RLQ analysis. How to interpret this?
## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Rjuv, dudiL = Ljuv, dudiQ = Qjuv, scannf = FALSE)
##
## Total inertia: 1.863
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 1.026449 0.591536 0.170240 0.060074 0.009378
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 55.1060 31.7572 9.1395 3.2251 0.5035
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 55.11 86.86 96.00 99.23 99.73
##
## (Only 5 dimensions (out of 10) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 1.0264493 1.0131383 1.159306 1.951706 0.4477715
## 2 0.5915357 0.7691136 1.330778 1.730192 0.3340340
##
## Inertia & coinertia R (Rjuv):
## inertia max ratio
## 1 1.343990 2.065940 0.6505464
## 12 3.114959 3.663509 0.8502666
##
## Inertia & coinertia Q (Qjuv):
## inertia max ratio
## 1 3.809156 5.920973 0.6433329
## 12 6.802721 8.827788 0.7706030
##
## Correlation L (Ljuv):
## corr max ratio
## 1 0.4477715 0.9445514 0.4740573
## 2 0.3340340 0.9087441 0.3675776## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Radu, dudiL = Ladu, dudiQ = Qadu, scannf = FALSE)
##
## Total inertia: 1.209
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.645060 0.394890 0.143635 0.014464 0.008915
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 53.3419 32.6546 11.8776 1.1961 0.7372
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 53.34 86.00 97.87 99.07 99.81
##
## (Only 5 dimensions (out of 11) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.6450601 0.8031564 1.359344 1.800936 0.3280747
## 2 0.3948903 0.6284030 1.165037 2.240272 0.2407674
##
## Inertia & coinertia R (Radu):
## inertia max ratio
## 1 1.847815 2.118831 0.8720918
## 12 3.205126 3.967985 0.8077466
##
## Inertia & coinertia Q (Qadu):
## inertia max ratio
## 1 3.243369 5.609379 0.5782047
## 12 8.262189 8.631936 0.9571652
##
## Correlation L (Ladu):
## corr max ratio
## 1 0.3280747 1.0000000 0.3280747
## 2 0.2407674 0.9128018 0.2637675Fourth-corner analysis
## [1] "FQ for juveniles"
## [1] "FQ for adults"
With adjusted p-values
## [1] "FQ for Juveniles"## [1] "FQ for Adults"
Combine both approaches
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 1.862683 0.4309029 greater 0.312
## 2 Model 4 1.862683 -0.3240938 greater 0.580
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 1.209293 14.908845364 greater 0.001
## 2 Model 4 1.209293 -0.004556487 greater 0.465
The total inertia of RLQ analysis is equal to the SRLQ multivariate statistic defined in Dray and Legendre (2008). This statistic is returned by the fourthcorner2 function:
## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envFORCOVER1, tabL = p_speciesJUV, tabQ = p_traits1,
## modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: 1.862683
##
## Based on 883 replicates
## Simulated p-value: 0.4852941
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## 3.648361e-01 -2.034443e+03 3.115231e+07## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envFORCOVER1, tabL = p_speciesADU, tabQ = p_traits1,
## modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: 1.209293
##
## Based on 999 replicates
## Simulated p-value: 0.431
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## 3.499361e-01 -1.878783e+03 2.886256e+07## [1] "juvenile"
## [1] "adult"
“Another approach is provided by the fourthcorner.rlq function and consists in testing directly the links between RLQ axes and traits (typetest=”Q.axes“) or environmental variables (typetest=”R.axes“).”
RLQ axes and traits
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.950193251 1.78473803 less
## 2 AxcR2 / Climb.0 Homog. 0.898922998 -0.42095161 less
## 3 AxcR1 / Climb.1 Homog. 0.049695209 -0.11445033 less
## 4 AxcR2 / Climb.1 Homog. 0.089668424 0.42121411 less
## 5 AxcR1 / Erect.0 Homog. 0.049695209 -0.11445033 less
## 6 AxcR2 / Erect.0 Homog. 0.089668424 0.42121411 less
## 7 AxcR1 / Erect.1 Homog. 0.950193251 1.78473803 less
## 8 AxcR2 / Erect.1 Homog. 0.898922998 -0.42095161 less
## 9 AxcR1 / StemS.0 Homog. 0.049695209 -0.59385264 less
## 10 AxcR2 / StemS.0 Homog. 0.089668424 0.42121411 less
## 11 AxcR1 / StemS.1 Homog. 0.368448080 -1.06661457 less
## 12 AxcR2 / StemS.1 Homog. 0.525133339 -0.12897045 less
## 13 AxcR1 / StemS.2 Homog. 0.403487598 3.43678672 less
## 14 AxcR2 / StemS.2 Homog. 0.371167341 2.88335254 less
## 15 AxcR1 / StemA.0 Homog. 0.847080961 3.09997508 less
## 16 AxcR2 / StemA.0 Homog. 0.560193193 -1.86718901 less
## 17 AxcR1 / StemA.1 Homog. 0.141642553 -0.18172266 less
## 18 AxcR2 / StemA.1 Homog. 0.312050411 1.35097765 less
## 19 AxcR1 / Leave.0 Homog. 0.797333053 3.40669292 less
## 20 AxcR2 / Leave.0 Homog. 0.468235999 -1.84730628 less
## 21 AxcR1 / Leave.1 Homog. 0.194270324 -0.25491466 less
## 22 AxcR2 / Leave.1 Homog. 0.460207772 2.41514864 less
## 23 AxcR1 / MaxStemHeight_m r -0.234799983 -1.34026471 two-sided
## 24 AxcR2 / MaxStemHeight_m r -0.066945580 -0.51622786 two-sided
## 25 AxcR1 / MaxStemDia_cm r -0.253003740 -1.42089696 two-sided
## 26 AxcR2 / MaxStemDia_cm r -0.035305477 -0.29971927 two-sided
## 27 AxcR1 / Under.canopy Homog. 0.979869766 0.66808379 less
## 28 AxcR2 / Under.canopy Homog. 0.981534581 0.95372648 less
## 29 AxcR1 / Under.understorey Homog. 0.018403668 -0.52356692 less
## 30 AxcR2 / Under.understorey Homog. 0.018394487 -0.52136764 less
## 31 AxcR1 / AverageFruitLength_cm r -0.451443234 -2.54658724 two-sided
## 32 AxcR2 / AverageFruitLength_cm r -0.004210788 -0.03114628 two-sided
## 33 AxcR1 / Fruit.large Homog. 0.325095192 1.27815147 less
## 34 AxcR2 / Fruit.large Homog. 0.476489677 2.26311991 less
## 35 AxcR1 / Fruit.small Homog. 0.550771380 3.01380670 less
## 36 AxcR2 / Fruit.small Homog. 0.523098288 2.51779907 less
## 37 AxcR1 / Consp.conspicuous Homog. 0.220090824 -1.60012966 less
## 38 AxcR2 / Consp.conspicuous Homog. 0.498734672 2.26617123 less
## 39 AxcR1 / Consp.cryptic Homog. 0.765977477 3.36043889 less
## 40 AxcR2 / Consp.cryptic Homog. 0.427568014 -0.34961875 less
## 41 AxcR1 / Endem.N Homog. 0.648448960 2.16671582 less
## 42 AxcR2 / Endem.N Homog. 0.671464239 2.50223484 less
## 43 AxcR1 / Endem.Y Homog. 0.248817870 0.63722025 less
## 44 AxcR2 / Endem.Y Homog. 0.310604637 1.00862386 less
## Pvalue Pvalue.adj
## 1 0.988 1
## 2 0.32 0.914064516129032
## 3 0.634593356242841 0.914064516129032
## 4 0.707 1
## 5 0.634593356242841 0.914064516129032
## 6 0.707 1
## 7 0.988 1
## 8 0.32 0.914064516129032
## 9 0.38109756097561 0.914064516129032
## 10 0.707 1
## 11 0.151 0.6908
## 12 0.481 0.914064516129032
## 13 0.997 1
## 14 0.985 1
## 15 1 1
## 16 0.07 0.513333333333333
## 17 0.493 0.914064516129032
## 18 0.914 1
## 19 1 1
## 20 0.038 0.418
## 21 0.424 0.914064516129032
## 22 0.996 1
## 23 0.19 0.76
## 24 0.639 1
## 25 0.157 0.6908
## 26 0.794 1
## 27 0.732 1
## 28 0.834 1
## 29 0.252595155709343 0.914064516129032
## 30 0.565167243367935 0.914064516129032
## 31 0.001 0.044 *
## 32 0.973 1
## 33 0.874 0.9614
## 34 0.992 0.992
## 35 0.996 1
## 36 0.983 1
## 37 0.053 0.4664
## 38 0.995 1
## 39 0.999 1
## 40 0.365 0.914064516129032
## 41 0.979 1
## 42 0.991 1
## 43 0.744 0.935314285714286
## 44 0.831 0.9614
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.839889789 -1.23610608 less
## 2 AxcR2 / Climb.0 Homog. 0.936177916 -0.02698244 less
## 3 AxcR1 / Climb.1 Homog. 0.065897849 0.20462341 less
## 4 AxcR2 / Climb.1 Homog. 0.061538793 0.04819169 less
## 5 AxcR1 / Erect.0 Homog. 0.065897849 0.20462341 less
## 6 AxcR2 / Erect.0 Homog. 0.061538793 0.04819169 less
## 7 AxcR1 / Erect.1 Homog. 0.839889789 -1.23610608 less
## 8 AxcR2 / Erect.1 Homog. 0.936177916 -0.02698244 less
## 9 AxcR1 / StemS.0 Homog. 0.084930906 1.69877200 less
## 10 AxcR2 / StemS.0 Homog. 0.072328995 -0.35370401 less
## 11 AxcR1 / StemS.1 Homog. 0.677673054 0.66732923 less
## 12 AxcR2 / StemS.1 Homog. 0.683558940 0.69941660 less
## 13 AxcR1 / StemS.2 Homog. 0.141382536 -0.97471883 less
## 14 AxcR2 / StemS.2 Homog. 0.214125410 -0.57182473 less
## 15 AxcR1 / StemA.0 Homog. 0.638291791 1.69089880 less
## 16 AxcR2 / StemA.0 Homog. 0.618650149 0.51642264 less
## 17 AxcR1 / StemA.1 Homog. 0.343059361 1.29931651 less
## 18 AxcR2 / StemA.1 Homog. 0.359912032 1.32198910 less
## 19 AxcR1 / Leave.0 Homog. 0.491428485 -1.75507695 less
## 20 AxcR2 / Leave.0 Homog. 0.556811983 0.56146161 less
## 21 AxcR1 / Leave.1 Homog. 0.508324379 2.30185705 less
## 22 AxcR2 / Leave.1 Homog. 0.428685041 1.22245129 less
## 23 AxcR1 / MaxStemHeight_m r 0.001987912 0.01365747 two-sided
## 24 AxcR2 / MaxStemHeight_m r 0.264466379 2.50320737 two-sided
## 25 AxcR1 / MaxStemDia_cm r 0.120705153 0.93414323 two-sided
## 26 AxcR2 / MaxStemDia_cm r 0.221464638 2.03959060 two-sided
## 27 AxcR1 / Under.canopy Homog. 0.924832221 -0.19345118 less
## 28 AxcR2 / Under.canopy Homog. 0.944938702 0.75394706 less
## 29 AxcR1 / Under.understorey Homog. 0.075157164 1.09449566 less
## 30 AxcR2 / Under.understorey Homog. 0.051982001 -0.03848357 less
## 31 AxcR1 / AverageFruitLength_cm r 0.051609120 0.43847120 two-sided
## 32 AxcR2 / AverageFruitLength_cm r 0.128240151 1.18518730 two-sided
## 33 AxcR1 / Fruit.large Homog. 0.479180668 2.30536632 less
## 34 AxcR2 / Fruit.large Homog. 0.547069452 2.71175647 less
## 35 AxcR1 / Fruit.small Homog. 0.510651838 2.37588150 less
## 36 AxcR2 / Fruit.small Homog. 0.430405233 -0.77704215 less
## 37 AxcR1 / Consp.conspicuous Homog. 0.569272801 1.82539825 less
## 38 AxcR2 / Consp.conspicuous Homog. 0.515477591 0.11928471 less
## 39 AxcR1 / Consp.cryptic Homog. 0.430411253 -0.34889375 less
## 40 AxcR2 / Consp.cryptic Homog. 0.461341932 -0.18664428 less
## 41 AxcR1 / Endem.N Homog. 0.775406254 4.96148018 less
## 42 AxcR2 / Endem.N Homog. 0.623975889 -1.42229751 less
## 43 AxcR1 / Endem.Y Homog. 0.206565714 0.26427154 less
## 44 AxcR2 / Endem.Y Homog. 0.339802139 1.23186183 less
## Pvalue Pvalue.adj
## 1 0.12 0.536
## 2 0.46 0.778461538461539
## 3 0.816503800217155 0.9691
## 4 0.740499457111835 0.9691
## 5 0.816503800217155 0.9691
## 6 0.740499457111835 0.9691
## 7 0.12 0.536
## 8 0.46 0.778461538461539
## 9 0.948 1
## 10 0.54 0.9691
## 11 0.716 0.9691
## 12 0.726 0.9691
## 13 0.213 0.754285714285714
## 14 0.336 0.829714285714286
## 15 0.955 1
## 16 0.703 0.893828571428571
## 17 0.881 0.9691
## 18 0.863 0.9691
## 19 0.052 0.4576
## 20 0.709 0.893828571428571
## 21 0.993 1
## 22 0.857 0.9691
## 23 0.987 1
## 24 0.004 0.132
## 25 0.38 0.829714285714286
## 26 0.026 0.33
## 27 0.355 0.829714285714286
## 28 0.75 0.916666666666667
## 29 0.855 1
## 30 0.736170212765957 0.9691
## 31 0.692 0.9691
## 32 0.266 0.780266666666667
## 33 0.971 0.993581395348837
## 34 0.995 0.995
## 35 0.992 1
## 36 0.215 0.473
## 37 0.972 1
## 38 0.53 0.9691
## 39 0.372 0.829714285714286
## 40 0.447 0.894
## 41 1 1
## 42 0.108 0.536
## 43 0.622 0.9691
## 44 0.841 0.9691
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1RLQ axes and environmental variables
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 Canopy.Cover / AxcQ1 r -0.005225042 -0.1046551 two-sided 0.904 0.939
## 2 Understory.Density / AxcQ1 r -0.039109377 -0.4276082 two-sided 0.727 0.912
## 3 Leaf.Litter / AxcQ1 r -0.011975126 -0.0811434 two-sided 0.939 0.939
## 4 Soil.Moisture / AxcQ1 r -0.213214982 -1.4974913 two-sided 0.146 0.581333333333333
## 5 Cec / AxcQ1 r -0.027025540 -0.3588843 two-sided 0.757 0.912
## 6 T50 / AxcQ1 r 0.044494996 0.6684522 two-sided 0.55 0.88
## 7 T10 / AxcQ1 r -0.300142333 -1.4469030 two-sided 0.161 0.644
## 8 Canopy.Height / AxcQ1 r 0.062674241 0.4163836 two-sided 0.76 0.912
## 9 Elevation / AxcQ1 r 0.075537324 0.4805011 two-sided 0.678 0.912
## 10 Habit.Primary / AxcQ1 Homog. 0.353990036 -1.3761412 less 0.104 0.624
## 11 Habit.Secondary / AxcQ1 Homog. 0.574188609 1.0303044 less 0.844 0.920727272727273
## 12 DIST_TO_EDGE / AxcQ1 r 0.219219415 1.3446398 two-sided 0.188 0.644571428571429
## 13 Canopy.Cover / AxcQ2 r -0.093816370 -1.2153270 two-sided 0.259 0.6672
## 14 Understory.Density / AxcQ2 r -0.203506782 -1.7770454 two-sided 0.065 0.39
## 15 Leaf.Litter / AxcQ2 r 0.151927905 1.1445878 two-sided 0.278 0.6672
## 16 Soil.Moisture / AxcQ2 r -0.094348556 -0.8294920 two-sided 0.457 0.88
## 17 Cec / AxcQ2 r 0.054931337 0.8941510 two-sided 0.388 0.846545454545454
## 18 T50 / AxcQ2 r 0.157686677 1.4317343 two-sided 0.2 0.581333333333333
## 19 T10 / AxcQ2 r 0.080736423 0.3717995 two-sided 0.695 0.912
## 20 Canopy.Height / AxcQ2 r -0.104820162 -0.7904038 two-sided 0.492 0.88
## 21 Elevation / AxcQ2 r 0.239858669 1.5881946 two-sided 0.134 0.6432
## 22 Habit.Primary / AxcQ2 Homog. 0.555681426 1.0340799 less 0.849 0.926181818181818
## 23 Habit.Secondary / AxcQ2 Homog. 0.444023222 -0.5910135 less 0.243 0.6672
## 24 DIST_TO_EDGE / AxcQ2 r -0.110392420 -0.6880360 two-sided 0.528 0.88
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 Canopy.Cover / AxcQ1 r -0.048167244 -1.0619662 two-sided 0.276 0.639272727272727
## 2 Understory.Density / AxcQ1 r -0.190393597 -1.9784619 two-sided 0.055 0.616
## 3 Leaf.Litter / AxcQ1 r 0.087803763 0.9900674 two-sided 0.405 0.694285714285714
## 4 Soil.Moisture / AxcQ1 r 0.162110244 1.5278285 two-sided 0.154 0.616
## 5 Cec / AxcQ1 r 0.039013207 0.8259116 two-sided 0.444 0.7104
## 6 T50 / AxcQ1 r -0.062618997 -1.5531882 two-sided 0.14 0.616
## 7 T10 / AxcQ1 r -0.035164882 -0.3926171 two-sided 0.683 0.885714285714286
## 8 Canopy.Height / AxcQ1 r 0.166388097 1.3863273 two-sided 0.142 0.616
## 9 Elevation / AxcQ1 r -0.267643184 -1.7624298 two-sided 0.098 0.616
## 10 Habit.Primary / AxcQ1 Homog. 0.627039627 5.2677663 less 1 1
## 11 Habit.Secondary / AxcQ1 Homog. 0.372950388 0.1609811 less 0.511 0.721411764705882
## 12 DIST_TO_EDGE / AxcQ1 r -0.142545392 -2.2004544 two-sided 0.02 0.48
## 13 Canopy.Cover / AxcQ2 r -0.039816375 -1.0777505 two-sided 0.293 0.639272727272727
## 14 Understory.Density / AxcQ2 r 0.003634773 0.1048194 two-sided 0.912 0.994909090909091
## 15 Leaf.Litter / AxcQ2 r 0.090431827 1.1069128 two-sided 0.322 0.644
## 16 Soil.Moisture / AxcQ2 r -0.104713419 -0.9198389 two-sided 0.381 0.694285714285714
## 17 Cec / AxcQ2 r -0.016003663 -0.2679409 two-sided 0.813 0.886909090909091
## 18 T50 / AxcQ2 r 0.010094780 0.2037692 two-sided 0.852 0.973714285714286
## 19 T10 / AxcQ2 r 0.159632657 1.3417132 two-sided 0.216 0.639272727272727
## 20 Canopy.Height / AxcQ2 r 0.167334976 1.3941289 two-sided 0.185 0.634285714285714
## 21 Elevation / AxcQ2 r 0.060347040 0.3755701 two-sided 0.745 0.885714285714286
## 22 Habit.Primary / AxcQ2 Homog. 0.684869599 7.2703433 less 1 1
## 23 Habit.Secondary / AxcQ2 Homog. 0.315108243 -0.6261314 less 0.277 0.639272727272727
## 24 DIST_TO_EDGE / AxcQ2 r -0.020856866 -0.3767687 two-sided 0.738 0.885714285714286
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Results can be represented using a table with colors indicating significance :
## [1] "juveniles"
## [1] "adults"
Significance with axes can also be reported on the factorial map of RLQ analysis. Here, significant associations with the first axis are represented in blue, with the second axis in orange, with both axes in green (variables with no significant association are in black)
## [1] "juveniles"
## [1] "adults"
RUN 4: RLQ/4th corner: Including Luke’s data, broken down by age, converted to Denisities
Run RLQ/ FQ analysis for all lifestage types COMBINED DATA
That’s unreadable, plotting as separate.
## [1] "RLQ for juveniles"
## [1] "RLQ for adults"
Summary of RLQ analysis. How to interpret this?
## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Rjuv, dudiL = Ljuv, dudiQ = Qjuv, scannf = FALSE)
##
## Total inertia: 0.5071
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.30533 0.11443 0.06096 0.02369 0.00200
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 60.2072 22.5644 12.0197 4.6722 0.3943
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 60.21 82.77 94.79 99.46 99.86
##
## (Only 5 dimensions (out of 8) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.3053304 0.5525671 1.063631 1.508370 0.3444183
## 2 0.1144315 0.3382772 1.111907 1.627049 0.1869837
##
## Inertia & coinertia R (Rjuv):
## inertia max ratio
## 1 1.131310 1.408984 0.8029265
## 12 2.367647 2.673132 0.8857201
##
## Inertia & coinertia Q (Qjuv):
## inertia max ratio
## 1 2.275181 3.708939 0.6134317
## 12 4.922468 6.934943 0.7098066
##
## Correlation L (Ljuv):
## corr max ratio
## 1 0.3444183 0.8781144 0.3922248
## 2 0.1869837 0.8370330 0.2233887## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Radu, dudiL = Ladu, dudiQ = Qadu, scannf = FALSE)
##
## Total inertia: 0.3568
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.192475 0.086756 0.067868 0.005586 0.002817
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 53.9414 24.3135 19.0201 1.5656 0.7894
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 53.94 78.25 97.27 98.84 99.63
##
## (Only 5 dimensions (out of 8) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.19247487 0.4387196 1.086161 1.913300 0.2111105
## 2 0.08675598 0.2945437 1.102252 1.403553 0.1903882
##
## Inertia & coinertia R (Radu):
## inertia max ratio
## 1 1.179745 1.387695 0.8501476
## 12 2.394704 2.740164 0.8739273
##
## Inertia & coinertia Q (Qadu):
## inertia max ratio
## 1 3.660716 4.077184 0.8978541
## 12 5.630678 7.312295 0.7700288
##
## Correlation L (Ladu):
## corr max ratio
## 1 0.2111105 1.0000000 0.2111105
## 2 0.1903882 0.9480088 0.2008296Fourth-corner analysis
## [1] "FQ for juveniles"
## [1] "FQ for adults"
With adjusted p-values
## [1] "FQ for Juveniles"## [1] "FQ for Adults"
Combine both approaches
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 0.507133 11.23012548 greater 0.001
## 2 Model 4 0.507133 0.06700219 greater 0.450
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 0.3568223 12.0699667 greater 0.001
## 2 Model 4 0.3568223 0.9624644 greater 0.174
The total inertia of RLQ analysis is equal to the SRLQ multivariate statistic defined in Dray and Legendre (2008). This statistic is returned by the fourthcorner2 function:
## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envCombined, tabL = JuvCombined, tabQ = p_traits2,
## modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: 0.507133
##
## Based on 943 replicates
## Simulated p-value: 0.4597458
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## 0.04949982 0.49969574 0.02257454## Monte-Carlo test
## Call: fourthcorner2(tabR = p_envCombined, tabL = AduCombined, tabQ = p_traits2,
## modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: 0.3568223
##
## Based on 999 replicates
## Simulated p-value: 0.166
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## 5.000727e-01 -2.399700e+03 2.303439e+07## [1] "juvenile"
## [1] "adult"
“Another approach is provided by the fourthcorner.rlq function and consists in testing directly the links between RLQ axes and traits (typetest=”Q.axes“) or environmental variables (typetest=”R.axes“).”
RLQ axes and traits
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.950691650 0.02297862 less
## 2 AxcR2 / Climb.0 Homog. 0.941841026 -0.16365303 less
## 3 AxcR1 / Climb.1 Homog. 0.033731565 -0.11523651 less
## 4 AxcR2 / Climb.1 Homog. 0.049479519 1.45852361 less
## 5 AxcR1 / Erect.0 Homog. 0.033731565 -0.11523651 less
## 6 AxcR2 / Erect.0 Homog. 0.049479519 1.45852361 less
## 7 AxcR1 / Erect.1 Homog. 0.950691650 0.02297862 less
## 8 AxcR2 / Erect.1 Homog. 0.941841026 -0.16365303 less
## 9 AxcR1 / StemS.0 Homog. 0.042486336 -0.62407515 less
## 10 AxcR2 / StemS.0 Homog. 0.059233726 1.32029688 less
## 11 AxcR1 / StemS.1 Homog. 0.600092020 0.06909407 less
## 12 AxcR2 / StemS.1 Homog. 0.663529348 0.98963052 less
## 13 AxcR1 / StemS.2 Homog. 0.337273734 1.95226449 less
## 14 AxcR2 / StemS.2 Homog. 0.267940716 -0.22206955 less
## 15 AxcR1 / StemA.0 Homog. 0.413618760 0.96874178 less
## 16 AxcR2 / StemA.0 Homog. 0.409856391 0.54901906 less
## 17 AxcR1 / StemA.1 Homog. 0.572991793 3.04965858 less
## 18 AxcR2 / StemA.1 Homog. 0.587847629 3.42208062 less
## 19 AxcR1 / Leave.0 Homog. 0.354248320 -0.12272264 less
## 20 AxcR2 / Leave.0 Homog. 0.353383576 -0.08334301 less
## 21 AxcR1 / Leave.1 Homog. 0.616579602 2.85114226 less
## 22 AxcR2 / Leave.1 Homog. 0.646520452 3.38539337 less
## 23 AxcR1 / MaxStemHeight_m r -0.081641368 -0.51410952 two-sided
## 24 AxcR2 / MaxStemHeight_m r 0.019080907 0.27036126 two-sided
## 25 AxcR1 / MaxStemDia_cm r -0.111440071 -0.69917296 two-sided
## 26 AxcR2 / MaxStemDia_cm r 0.051767377 0.65718792 two-sided
## 27 AxcR1 / Under.canopy Homog. 0.825995793 -0.21400969 less
## 28 AxcR2 / Under.canopy Homog. 0.824299326 -0.29534801 less
## 29 AxcR1 / Under.understorey Homog. 0.131796389 -0.01477115 less
## 30 AxcR2 / Under.understorey Homog. 0.173736036 0.37677877 less
## 31 AxcR1 / AverageFruitLength_cm r 0.003639056 0.03905259 two-sided
## 32 AxcR2 / AverageFruitLength_cm r 0.139110582 1.60663803 two-sided
## 33 AxcR1 / Fruit.large Homog. 0.171370100 -0.07021277 less
## 34 AxcR2 / Fruit.large Homog. 0.225979472 0.40238496 less
## 35 AxcR1 / Fruit.small Homog. 0.816271465 3.55292068 less
## 36 AxcR2 / Fruit.small Homog. 0.742787554 -0.65533486 less
## 37 AxcR1 / Consp.conspicuous Homog. 0.665815314 1.43610990 less
## 38 AxcR2 / Consp.conspicuous Homog. 0.699872302 1.90444340 less
## 39 AxcR1 / Consp.cryptic Homog. 0.317460710 0.87173520 less
## 40 AxcR2 / Consp.cryptic Homog. 0.298427569 -0.28843876 less
## 41 AxcR1 / Endem.N Homog. 0.722721789 -0.14631779 less
## 42 AxcR2 / Endem.N Homog. 0.720851064 -0.26717447 less
## 43 AxcR1 / Endem.Y Homog. 0.191637919 -0.40711010 less
## 44 AxcR2 / Endem.Y Homog. 0.272932571 0.59682909 less
## Pvalue Pvalue.adj
## 1 0.342 0.875111111111111
## 2 0.45 0.875111111111111
## 3 0.680896478121665 0.881160148157449
## 4 0.931 0.985395348837209
## 5 0.680896478121665 0.881160148157449
## 6 0.931 0.985395348837209
## 7 0.342 0.875111111111111
## 8 0.45 0.875111111111111
## 9 0.345 0.875111111111111
## 10 0.908 0.985395348837209
## 11 0.493 0.875111111111111
## 12 0.855 0.985395348837209
## 13 0.963 0.985395348837209
## 14 0.428 0.875111111111111
## 15 0.824 0.979891891891892
## 16 0.725 0.935314285714286
## 17 0.999 1
## 18 1 1
## 19 0.461 0.743285714285714
## 20 0.473 0.743285714285714
## 21 0.997 1
## 22 1 1
## 23 0.649 0.881160148157449
## 24 0.81 0.963243243243243
## 25 0.514 0.875111111111111
## 26 0.535 0.875111111111111
## 27 0.352 0.875111111111111
## 28 0.368 0.875111111111111
## 29 0.568 0.881160148157449
## 30 0.647 0.881160148157449
## 31 0.978 1
## 32 0.102 0.641142857142857
## 33 0.537 0.875111111111111
## 34 0.652 0.881160148157449
## 35 1 1
## 36 0.245 0.875111111111111
## 37 0.924 1
## 38 0.976 1
## 39 0.796 0.972888888888889
## 40 0.396 0.69696
## 41 0.422 0.875111111111111
## 42 0.394 0.875111111111111
## 43 0.389 0.875111111111111
## 44 0.744 0.935314285714286
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.97179858 0.914152396 less
## 2 AxcR2 / Climb.0 Homog. 0.97948921 2.604089304 less
## 3 AxcR1 / Climb.1 Homog. 0.02531189 -0.352455173 less
## 4 AxcR2 / Climb.1 Homog. 0.01348188 -0.589989143 less
## 5 AxcR1 / Erect.0 Homog. 0.02531189 -0.352455173 less
## 6 AxcR2 / Erect.0 Homog. 0.01348188 -0.589989143 less
## 7 AxcR1 / Erect.1 Homog. 0.97179858 0.914152396 less
## 8 AxcR2 / Erect.1 Homog. 0.97948921 2.604089304 less
## 9 AxcR1 / StemS.0 Homog. 0.04679292 -0.460331662 less
## 10 AxcR2 / StemS.0 Homog. 0.04346445 -0.591578392 less
## 11 AxcR1 / StemS.1 Homog. 0.47268434 -0.679161415 less
## 12 AxcR2 / StemS.1 Homog. 0.53370050 3.049384513 less
## 13 AxcR1 / StemS.2 Homog. 0.46353583 0.994016377 less
## 14 AxcR2 / StemS.2 Homog. 0.41647109 0.851510796 less
## 15 AxcR1 / StemA.0 Homog. 0.21466306 -1.191998737 less
## 16 AxcR2 / StemA.0 Homog. 0.29338290 3.790097450 less
## 17 AxcR1 / StemA.1 Homog. 0.78478607 1.201653576 less
## 18 AxcR2 / StemA.1 Homog. 0.69891091 3.317531288 less
## 19 AxcR1 / Leave.0 Homog. 0.18698199 -0.871186511 less
## 20 AxcR2 / Leave.0 Homog. 0.26528813 4.371985909 less
## 21 AxcR1 / Leave.1 Homog. 0.81301791 0.915403428 less
## 22 AxcR2 / Leave.1 Homog. 0.71751015 2.856201824 less
## 23 AxcR1 / MaxStemHeight_m r -0.11128831 -1.473647834 two-sided
## 24 AxcR2 / MaxStemHeight_m r -0.04326206 -0.598501338 two-sided
## 25 AxcR1 / MaxStemDia_cm r -0.16305380 -2.163140637 two-sided
## 26 AxcR2 / MaxStemDia_cm r -0.02330345 -0.293644047 two-sided
## 27 AxcR1 / Under.canopy Homog. 0.84135842 -0.061285857 less
## 28 AxcR2 / Under.canopy Homog. 0.84882465 0.912217124 less
## 29 AxcR1 / Under.understorey Homog. 0.15371029 0.063375226 less
## 30 AxcR2 / Under.understorey Homog. 0.14529232 -0.001334491 less
## 31 AxcR1 / AverageFruitLength_cm r -0.20867857 -2.765443755 two-sided
## 32 AxcR2 / AverageFruitLength_cm r 0.03378664 0.527096705 two-sided
## 33 AxcR1 / Fruit.large Homog. 0.21701516 0.134072032 less
## 34 AxcR2 / Fruit.large Homog. 0.22896442 0.253936793 less
## 35 AxcR1 / Fruit.small Homog. 0.74297350 -0.364222176 less
## 36 AxcR2 / Fruit.small Homog. 0.76496435 -0.263594037 less
## 37 AxcR1 / Consp.conspicuous Homog. 0.76188172 1.391075196 less
## 38 AxcR2 / Consp.conspicuous Homog. 0.72621006 1.411520681 less
## 39 AxcR1 / Consp.cryptic Homog. 0.23058913 -0.512603616 less
## 40 AxcR2 / Consp.cryptic Homog. 0.27337586 1.916362313 less
## 41 AxcR1 / Endem.N Homog. 0.83942871 0.420995017 less
## 42 AxcR2 / Endem.N Homog. 0.85125177 1.396776241 less
## 43 AxcR1 / Endem.Y Homog. 0.15572888 -0.514687259 less
## 44 AxcR2 / Endem.Y Homog. 0.13859593 -0.751428706 less
## Pvalue Pvalue.adj
## 1 0.819 1
## 2 0.999 1
## 3 0.50308261405672 0.870941176470588
## 4 0.316892725030826 0.870941176470588
## 5 0.50308261405672 0.870941176470588
## 6 0.316892725030826 0.870941176470588
## 7 0.819 1
## 8 0.999 1
## 9 0.425334706488157 0.870941176470588
## 10 0.377960865087539 0.870941176470588
## 11 0.305 0.870941176470588
## 12 1 1
## 13 0.78 0.91821052631579
## 14 0.793 0.91821052631579
## 15 0.112 0.289882352941176
## 16 1 1
## 17 0.893 1
## 18 1 1
## 19 0.191 0.442315789473684
## 20 1 1
## 21 0.823 1
## 22 1 1
## 23 0.155 0.757777777777778
## 24 0.569 0.870941176470588
## 25 0.02 0.146666666666667
## 26 0.77 0.91821052631579
## 27 0.324 0.870941176470588
## 28 0.82 1
## 29 0.670670670670671 0.870941176470588
## 30 0.607607607607608 0.870941176470588
## 31 0.002 0.0176 *
## 32 0.581 0.870941176470588
## 33 0.673 0.870941176470588
## 34 0.655 0.870941176470588
## 35 0.254 0.870941176470588
## 36 0.343 0.870941176470588
## 37 0.924 1
## 38 0.924 1
## 39 0.321 0.614086956521739
## 40 0.962 1
## 41 0.648 0.891
## 42 0.92 1
## 43 0.388 0.870941176470588
## 44 0.266 0.870941176470588
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1RLQ axes and environmental variables
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 Under.dense / AxcQ1 Homog. 0.221464258 0.327772208 less 0.743 0.8916
## 2 Under.low / AxcQ1 Homog. 0.218403774 -0.813982319 less 0.191 0.42975
## 3 Under.medium / AxcQ1 Homog. 0.550063386 1.365268845 less 0.923 0.997
## 4 Cec / AxcQ1 r 0.042828674 1.293053664 two-sided 0.123 0.339428571428571
## 5 T50 / AxcQ1 r -0.000714878 0.007297674 two-sided 0.997 0.997
## 6 T10 / AxcQ1 r -0.026242242 -0.815171179 two-sided 0.397 0.7146
## 7 Canopy.Height / AxcQ1 r -0.043252066 -0.639468467 two-sided 0.54 0.694285714285714
## 8 Elevation / AxcQ1 r 0.343316027 2.188200528 two-sided 0.009 0.108
## 9 DIST_TO_EDGE / AxcQ1 r 0.043264696 0.712888388 two-sided 0.506 0.694285714285714
## 10 Under.dense / AxcQ2 Homog. 0.271414040 2.285892891 less 0.978 0.997
## 11 Under.low / AxcQ2 Homog. 0.208125884 -1.563276630 less 0.061 0.216
## 12 Under.medium / AxcQ2 Homog. 0.513648363 0.136618803 less 0.501 0.7515
## 13 Cec / AxcQ2 r -0.043906956 -1.249087138 two-sided 0.132 0.339428571428571
## 14 T50 / AxcQ2 r -0.017580374 -0.500141307 two-sided 0.554 0.767076923076923
## 15 T10 / AxcQ2 r 0.024502707 0.711369310 two-sided 0.464 0.7515
## 16 Canopy.Height / AxcQ2 r 0.153488306 2.266352612 two-sided 0.012 0.108
## 17 Elevation / AxcQ2 r 0.019284269 0.162401495 two-sided 0.894 0.986
## 18 DIST_TO_EDGE / AxcQ2 r 0.098216141 1.802778491 two-sided 0.071 0.216
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 Under.dense / AxcQ1 Homog. 0.214360348 -0.03128674 less 0.502 0.695076923076923
## 2 Under.low / AxcQ1 Homog. 0.306199419 1.62081624 less 0.974 0.974
## 3 Under.medium / AxcQ1 Homog. 0.476937675 -1.30113594 less 0.103 0.3708
## 4 Cec / AxcQ1 r 0.031433924 1.12053990 two-sided 0.264 0.396
## 5 T50 / AxcQ1 r -0.007846279 -0.27933305 two-sided 0.779 0.876375
## 6 T10 / AxcQ1 r -0.132361714 -1.99303642 two-sided 0.01 0.066 .
## 7 Canopy.Height / AxcQ1 r -0.152381058 -1.91431680 two-sided 0.011 0.066 .
## 8 Elevation / AxcQ1 r 0.084566234 1.25240235 two-sided 0.224 0.504
## 9 DIST_TO_EDGE / AxcQ1 r -0.033692825 -0.45611548 two-sided 0.73 0.846
## 10 Under.dense / AxcQ2 Homog. 0.233712304 0.57698290 less 0.745 0.876375
## 11 Under.low / AxcQ2 Homog. 0.286539392 0.38202529 less 0.66 0.848571428571429
## 12 Under.medium / AxcQ2 Homog. 0.476587859 -1.02035920 less 0.167 0.429428571428571
## 13 Cec / AxcQ2 r -0.005443898 -0.16437119 two-sided 0.854 0.899
## 14 T50 / AxcQ2 r -0.030475271 -0.94304199 two-sided 0.352 0.6336
## 15 T10 / AxcQ2 r 0.036422985 0.53148379 two-sided 0.675 0.846
## 16 Canopy.Height / AxcQ2 r 0.050444774 0.62290993 two-sided 0.613 0.846
## 17 Elevation / AxcQ2 r 0.175774038 2.57900815 two-sided 0.006 0.066 .
## 18 DIST_TO_EDGE / AxcQ2 r 0.071782890 1.05208457 two-sided 0.336 0.6336
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Results can be represented using a table with colors indicating significance :
## [1] "juveniles"
## [1] "adults"
Significance with axes can also be reported on the factorial map of RLQ analysis. Here, significant associations with the first axis are represented in blue, with the second axis in orange, with both axes in green (variables with no significant association are in black)
## [1] "juveniles"
## [1] "adults"
RUN 5: Only Luke’s data as abundances
## 'data.frame': 19 obs. of 12 variables:
## $ Climbing : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 2 1 ...
## $ Erect : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 1 2 ...
## $ StemSolitary : Factor w/ 3 levels "0","1","2": 2 2 2 3 3 3 2 2 1 3 ...
## $ StemArmed : Factor w/ 2 levels "0","1": 2 2 1 2 2 2 1 1 1 1 ...
## $ LeavesArmed : Factor w/ 2 levels "0","1": 2 2 1 2 2 2 1 1 2 1 ...
## $ MaxStemHeight_m : num 4.5 15 35 10 18 10 10 4.5 20 3 ...
## $ MaxStemDia_cm : num 6 30 60 8 25 10 8 3 3 3.4 ...
## $ UnderstoreyCanopy : Factor w/ 2 levels "canopy","understorey": 2 1 1 1 1 1 1 2 1 2 ...
## $ AverageFruitLength_cm: num 0.75 5.5 5 2 5 ...
## $ FruitSizeCategorical : Factor w/ 2 levels "large","small": 2 1 1 2 1 2 2 2 2 2 ...
## $ Conspicuousness : Factor w/ 2 levels "conspicuous",..: 2 1 2 1 1 1 1 2 1 2 ...
## $ Endemic : Factor w/ 2 levels "N","Y": 2 1 2 1 1 1 1 1 1 1 ...## 'data.frame': 2300 obs. of 7 variables:
## $ ELEV : num 414 413 412 411 411 409 407 406 405 405 ...
## $ DIST_TO_EDGE: num 1.5 6 11.4 16.6 23.3 28.5 33.5 38.2 40.6 44.2 ...
## $ CANOPY : num 25 25 31 28 25 23 7 21 25 20 ...
## $ TEN : num 5 3 4 3 5 5 4 4 4 5 ...
## $ FIFTY : num 0 0 0 1 0 0 0 0 0 0 ...
## $ CECR : num 0 0 0 0 0 0 0 0 1 0 ...
## $ UNDERSTORY : Factor w/ 3 levels "dense","low",..: 1 1 1 1 1 1 1 3 3 3 ...## 'data.frame': 2300 obs. of 19 variables:
## $ AST : num 0 0 0 0 1 0 0 0 0 0 ...
## $ AT : num 0 0 0 0 0 0 0 0 0 0 ...
## $ ATT : num 0 0 0 0 0 0 0 0 0 0 ...
## $ BATCO: num 0 0 0 0 0 0 0 3 0 0 ...
## $ BATSE: num 0 0 0 0 0 0 0 0 0 0 ...
## $ BG : num 0 0 0 0 0 0 0 0 0 0 ...
## $ CHAM : num 0 0 0 0 0 0 0 0 0 0 ...
## $ CP : num 0 0 0 0 0 0 0 0 0 0 ...
## $ DESM : num 0 0 0 0 0 0 0 0 0 0 ...
## $ IR : num 0 0 1 0 1 0 0 0 2 0 ...
## $ ONE : num 0 2 0 2 2 0 0 0 0 0 ...
## $ PHD : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PHOL : num 1 0 2 0 0 0 0 0 0 0 ...
## $ PRDE : num 0 0 0 0 0 0 0 0 0 0 ...
## $ SOC : num 0 0 0 0 0 0 0 1 0 1 ...
## $ SYN : num 0 0 1 0 0 0 0 1 0 0 ...
## $ TAG : num 0 0 1 3 2 0 0 0 0 0 ...
## $ WET : num 0 0 0 0 0 0 0 0 0 0 ...
## $ GO : num 0 0 1 0 1 0 0 0 1 0 ...## 'data.frame': 2300 obs. of 18 variables:
## $ AST : num 0 0 0 0 0 0 0 0 0 0 ...
## $ AT : num 0 0 0 0 0 0 0 0 0 0 ...
## $ BATCO: num 0 0 0 0 0 0 0 0 0 0 ...
## $ BATSE: num 0 0 0 0 0 0 0 0 0 0 ...
## $ BG : num 0 0 0 0 0 0 0 0 0 0 ...
## $ CHAM : num 0 0 0 0 0 0 0 0 0 0 ...
## $ CP : num 0 0 0 1 0 0 0 0 0 0 ...
## $ DESM : num 0 0 0 0 0 0 0 0 0 0 ...
## $ IR : num 0 0 0 0 0 0 0 0 0 1 ...
## $ ONE : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PHD : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PHOL : num 0 0 0 0 0 0 0 0 0 0 ...
## $ PRDE : num 0 0 0 0 0 0 0 0 0 0 ...
## $ SOC : num 0 0 0 0 0 0 0 0 0 0 ...
## $ SYN : num 0 0 0 0 0 0 0 0 0 0 ...
## $ TAG : num 0 0 0 0 0 0 0 0 0 0 ...
## $ WET : num 0 0 0 0 0 0 0 0 0 0 ...
## $ GO : num 0 0 0 0 0 0 0 0 0 0 ...## Climbing Erect StemSolitary StemArmed LeavesArmed MaxStemHeight_m
## AT 0 1 1 1 1 4.5
## AST 0 1 1 1 1 15.0
## BATCO 0 1 2 1 1 10.0
## BG 0 1 2 1 1 18.0
## BATSE 0 1 2 1 1 10.0
## CHAM 0 1 1 0 0 10.0
## CP 0 1 1 0 0 4.5
## DESM 1 0 0 0 1 20.0
## GO 0 1 2 0 0 3.0
## IR 0 1 1 0 0 30.0
## ONE 0 1 1 0 0 26.0
## PHD 0 1 1 0 0 10.0
## PHOL 0 1 1 0 0 12.0
## TAG 0 1 1 0 0 15.0
## PRDE 0 1 2 0 0 10.0
## SOC 0 1 1 0 0 20.0
## SYN 0 1 0 0 0 6.0
## WET 0 1 1 0 0 10.0
## MaxStemDia_cm UnderstoreyCanopy AverageFruitLength_cm
## AT 6.0 understorey 0.750
## AST 30.0 canopy 5.500
## BATCO 8.0 canopy 2.000
## BG 25.0 canopy 5.000
## BATSE 10.0 canopy 1.900
## CHAM 8.0 canopy 1.650
## CP 3.0 understorey 1.250
## DESM 3.0 canopy 1.823
## GO 3.4 understorey 0.760
## IR 70.0 canopy 2.350
## ONE 45.0 canopy 3.500
## PHD 12.0 canopy 1.215
## PHOL 22.0 canopy 1.385
## TAG 30.0 canopy 7.500
## PRDE 12.0 canopy 0.900
## SOC 20.0 canopy 3.000
## SYN 5.0 canopy 2.350
## WET 13.0 canopy 2.500
## FruitSizeCategorical Conspicuousness Endemic
## AT small cryptic Y
## AST large conspicuous N
## BATCO small conspicuous N
## BG large conspicuous N
## BATSE small conspicuous N
## CHAM small conspicuous N
## CP small cryptic N
## DESM small conspicuous N
## GO small cryptic N
## IR small conspicuous N
## ONE small cryptic N
## PHD small conspicuous Y
## PHOL small cryptic N
## TAG large cryptic Y
## PRDE small cryptic N
## SOC small cryptic N
## SYN small conspicuous N
## WET small conspicuous YRun RLQ/ FQ analysis for all lifestage types COMBINED DATA
That’s unreadable, plotting as separate.
## [1] "RLQ for juveniles"
## [1] "RLQ for adults"
Summary of RLQ analysis. How to interpret this?
## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Rjuv, dudiL = Ljuv, dudiQ = Qjuv, scannf = FALSE)
##
## Total inertia: 0.3496
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.253201 0.051745 0.029468 0.009449 0.002748
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 72.431 14.802 8.430 2.703 0.786
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 72.43 87.23 95.66 98.37 99.15
##
## (Only 5 dimensions (out of 8) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.25320147 0.5031913 1.102316 1.462761 0.3120711
## 2 0.05174511 0.2274755 1.017318 1.356392 0.1648515
##
## Inertia & coinertia R (Rjuv):
## inertia max ratio
## 1 1.215101 1.427770 0.8510478
## 12 2.250036 2.706504 0.8313439
##
## Inertia & coinertia Q (Qjuv):
## inertia max ratio
## 1 2.139670 3.800487 0.5629991
## 12 3.979469 6.041936 0.6586413
##
## Correlation L (Ljuv):
## corr max ratio
## 1 0.3120711 0.8790003 0.3550296
## 2 0.1648515 0.8158605 0.2020585## RLQ analysis
##
## Class: rlq dudi
## Call: rlq(dudiR = Radu, dudiL = Ladu, dudiQ = Qadu, scannf = FALSE)
##
## Total inertia: 0.2272
##
## Eigenvalues:
## Ax1 Ax2 Ax3 Ax4 Ax5
## 0.112675 0.083210 0.014000 0.008495 0.006291
##
## Projected inertia (%):
## Ax1 Ax2 Ax3 Ax4 Ax5
## 49.583 36.617 6.161 3.738 2.768
##
## Cumulative projected inertia (%):
## Ax1 Ax1:2 Ax1:3 Ax1:4 Ax1:5
## 49.58 86.20 92.36 96.10 98.87
##
## (Only 5 dimensions (out of 8) are shown)
##
##
## Eigenvalues decomposition:
## eig covar sdR sdQ corr
## 1 0.11267484 0.3356707 0.9879998 1.643250 0.2067535
## 2 0.08320955 0.2884607 1.1240015 1.863746 0.1376997
##
## Inertia & coinertia R (Radu):
## inertia max ratio
## 1 0.9761436 1.532974 0.6367647
## 12 2.2395230 2.712636 0.8255891
##
## Inertia & coinertia Q (Qadu):
## inertia max ratio
## 1 2.700272 4.108066 0.6573099
## 12 6.173821 6.921196 0.8920166
##
## Correlation L (Ladu):
## corr max ratio
## 1 0.2067535 0.9773324 0.2115488
## 2 0.1376997 0.9603342 0.1433873Fourth-corner analysis
## [1] "FQ for juveniles"
## [1] "FQ for adults"
With adjusted p-values
## [1] "FQ for Juveniles"## [1] "FQ for Adults"
Combine both approaches
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 0.3495769 5.294913 greater 0.003
## 2 Model 4 0.3495769 -1.001535 greater 0.841
## class: krandtest lightkrandtest
## Monte-Carlo tests
## Call: randtest.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6)
##
## Number of tests: 2
##
## Adjustment method for multiple comparisons: none
## Permutation number: 999
## Test Obs Std.Obs Alter Pvalue
## 1 Model 2 0.227245 2.1173563 greater 0.032
## 2 Model 4 0.227245 -0.8647113 greater 0.809
The total inertia of RLQ analysis is equal to the SRLQ multivariate statistic defined in Dray and Legendre (2008). This statistic is returned by the fourthcorner2 function:
## Monte-Carlo test
## Call: fourthcorner2(tabR = tempLukeENV, tabL = tempLukeP_juv, tabQ = p_traits3,
## modeltype = 6, nrepet = nrepet, p.adjust.method.G = "fdr")
##
## Observation: 0.3495769
##
## Based on 999 replicates
## Simulated p-value: 0.837
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## -0.9950583 0.5070412 0.0250419## Monte-Carlo test
## Call: fourthcorner2(tabR = tempLukeENV, tabL = tempLukeP_ad, tabQ = subset(p_traits3,
## rownames(p_traits3) != "ATT"), modeltype = 6, nrepet = nrepet,
## p.adjust.method.G = "fdr")
##
## Observation: 0.227245
##
## Based on 999 replicates
## Simulated p-value: 0.782
## Alternative hypothesis: greater
##
## Std.Obs Expectation Variance
## -0.830801471 0.277645441 0.003680229## [1] "juvenile"
## [1] "adult"
“Another approach is provided by the fourthcorner.rlq function and consists in testing directly the links between RLQ axes and traits (typetest=”Q.axes“) or environmental variables (typetest=”R.axes“).”
RLQ axes and traits
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.9987687707 0.88682739 less
## 2 AxcR2 / Climb.0 Homog. 0.9987476602 0.99016069 less
## 3 AxcR1 / Climb.1 Homog. 0.0008108668 -0.32899201 less
## 4 AxcR2 / Climb.1 Homog. 0.0003319984 -0.98527357 less
## 5 AxcR1 / Erect.0 Homog. 0.0008108668 -0.32899201 less
## 6 AxcR2 / Erect.0 Homog. 0.0003319984 -0.98527357 less
## 7 AxcR1 / Erect.1 Homog. 0.9987687707 0.88682739 less
## 8 AxcR2 / Erect.1 Homog. 0.9987476602 0.99016069 less
## 9 AxcR1 / StemS.0 Homog. 0.0450451117 -0.61118930 less
## 10 AxcR2 / StemS.0 Homog. 0.0476509254 -0.79087050 less
## 11 AxcR1 / StemS.1 Homog. 0.7430481116 2.76091522 less
## 12 AxcR2 / StemS.1 Homog. 0.7086722442 0.69530715 less
## 13 AxcR1 / StemS.2 Homog. 0.1889971996 -0.53878978 less
## 14 AxcR2 / StemS.2 Homog. 0.2372120489 -0.24498835 less
## 15 AxcR1 / StemA.0 Homog. 0.9512348914 2.69794755 less
## 16 AxcR2 / StemA.0 Homog. 0.9558284108 2.64687294 less
## 17 AxcR1 / StemA.1 Homog. 0.0456234804 -1.88476111 less
## 18 AxcR2 / StemA.1 Homog. 0.0427127561 -2.18423441 less
## 19 AxcR1 / Leave.0 Homog. 0.9500246343 2.66787336 less
## 20 AxcR2 / Leave.0 Homog. 0.9545544131 2.61283954 less
## 21 AxcR1 / Leave.1 Homog. 0.0472049444 -2.24577836 less
## 22 AxcR2 / Leave.1 Homog. 0.0436668939 -2.58334353 less
## 23 AxcR1 / MaxStemHeight_m r -0.0056327444 -0.10883613 two-sided
## 24 AxcR2 / MaxStemHeight_m r -0.1036183894 -1.62913691 two-sided
## 25 AxcR1 / MaxStemDia_cm r 0.0585498660 0.43073260 two-sided
## 26 AxcR2 / MaxStemDia_cm r -0.1606342290 -2.95547643 two-sided
## 27 AxcR1 / Under.canopy Homog. 0.8734630866 3.53595591 less
## 28 AxcR2 / Under.canopy Homog. 0.8480620518 0.86129364 less
## 29 AxcR1 / Under.understorey Homog. 0.1260046718 -0.14715570 less
## 30 AxcR2 / Under.understorey Homog. 0.1507807032 -0.08355338 less
## 31 AxcR1 / AverageFruitLength_cm r -0.2271876191 -1.34660127 two-sided
## 32 AxcR2 / AverageFruitLength_cm r -0.0026733621 -0.06479005 two-sided
## 33 AxcR1 / Fruit.large Homog. 0.1822455527 -0.08507815 less
## 34 AxcR2 / Fruit.large Homog. 0.1412713332 -0.71455933 less
## 35 AxcR1 / Fruit.small Homog. 0.7479025293 -0.33449854 less
## 36 AxcR2 / Fruit.small Homog. 0.8584962461 2.26104800 less
## 37 AxcR1 / Consp.conspicuous Homog. 0.3201754800 0.06716201 less
## 38 AxcR2 / Consp.conspicuous Homog. 0.3921603600 2.86361708 less
## 39 AxcR1 / Consp.cryptic Homog. 0.6588325370 1.59024693 less
## 40 AxcR2 / Consp.cryptic Homog. 0.6074045296 1.16697737 less
## 41 AxcR1 / Endem.N Homog. 0.6367268132 -0.85639175 less
## 42 AxcR2 / Endem.N Homog. 0.7368704921 2.45061784 less
## 43 AxcR1 / Endem.Y Homog. 0.3310067021 0.85285614 less
## 44 AxcR2 / Endem.Y Homog. 0.2630461434 0.03652826 less
## Pvalue Pvalue.adj
## 1 0.952 1
## 2 0.884 1
## 3 0.458 0.719714285714286
## 4 0.049 0.308
## 5 0.458 0.719714285714286
## 6 0.049 0.308
## 7 0.952 1
## 8 0.884 1
## 9 0.373 0.863789473684211
## 10 0.298 0.8195
## 11 0.992 1
## 12 0.738 1
## 13 0.325 0.823777777777778
## 14 0.433 0.925692307692308
## 15 0.998 1
## 16 0.996 1
## 17 0.004 0.044 *
## 18 0.005 0.044 *
## 19 0.999 1
## 20 0.996 1
## 21 0.001 0.022 *
## 22 0.002 0.0293333333333333 *
## 23 0.926 1
## 24 0.09 0.44
## 25 0.704 1
## 26 0.007 0.0308 *
## 27 1 1
## 28 0.821 1
## 29 0.508 0.925692307692308
## 30 0.491 0.925692307692308
## 31 0.188 0.636307692307692
## 32 0.945 1
## 33 0.523 0.925692307692308
## 34 0.249 0.7304
## 35 0.337 0.823777777777778
## 36 1 1
## 37 0.552 0.809032258064516
## 38 0.989 1
## 39 0.937 1
## 40 0.878 1
## 41 0.212 0.666285714285714
## 42 0.999 1
## 43 0.814 1
## 44 0.547 0.925692307692308
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "Q.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter
## 1 AxcR1 / Climb.0 Homog. 0.9991347824 0.65487938 less
## 2 AxcR2 / Climb.0 Homog. 0.9986996548 0.61722337 less
## 3 AxcR1 / Climb.1 Homog. 0.0003177235 -0.44855971 less
## 4 AxcR2 / Climb.1 Homog. 0.0005084710 -0.22805059 less
## 5 AxcR1 / Erect.0 Homog. 0.0003177235 -0.44855971 less
## 6 AxcR2 / Erect.0 Homog. 0.0005084710 -0.22805059 less
## 7 AxcR1 / Erect.1 Homog. 0.9991347824 0.65487938 less
## 8 AxcR2 / Erect.1 Homog. 0.9986996548 0.61722337 less
## 9 AxcR1 / StemS.0 Homog. 0.0213369430 -0.71889219 less
## 10 AxcR2 / StemS.0 Homog. 0.0276319001 -0.63837652 less
## 11 AxcR1 / StemS.1 Homog. 0.6665462592 0.33491920 less
## 12 AxcR2 / StemS.1 Homog. 0.6331971702 0.14002055 less
## 13 AxcR1 / StemS.2 Homog. 0.2845234073 0.12382590 less
## 14 AxcR2 / StemS.2 Homog. 0.3202676786 0.32619963 less
## 15 AxcR1 / StemA.0 Homog. 0.9102057866 1.14443704 less
## 16 AxcR2 / StemA.0 Homog. 0.9211187280 1.14962293 less
## 17 AxcR1 / StemA.1 Homog. 0.0611473154 -1.25096409 less
## 18 AxcR2 / StemA.1 Homog. 0.0779316181 0.07817659 less
## 19 AxcR1 / Leave.0 Homog. 0.9094298340 1.41392210 less
## 20 AxcR2 / Leave.0 Homog. 0.9197977076 1.39764104 less
## 21 AxcR1 / Leave.1 Homog. 0.0635809214 -1.04251740 less
## 22 AxcR2 / Leave.1 Homog. 0.0790007011 0.04882859 less
## 23 AxcR1 / MaxStemHeight_m r -0.0624278693 -0.59096454 two-sided
## 24 AxcR2 / MaxStemHeight_m r 0.0884008818 0.93645805 two-sided
## 25 AxcR1 / MaxStemDia_cm r -0.0242877015 -0.15589571 two-sided
## 26 AxcR2 / MaxStemDia_cm r 0.0927305433 1.03739751 two-sided
## 27 AxcR1 / Under.canopy Homog. 0.8111248473 0.96310258 less
## 28 AxcR2 / Under.canopy Homog. 0.7772226093 -0.40410675 less
## 29 AxcR1 / Under.understorey Homog. 0.1868817567 0.24621328 less
## 30 AxcR2 / Under.understorey Homog. 0.2116166257 0.39975532 less
## 31 AxcR1 / AverageFruitLength_cm r -0.0469149117 -0.35465609 two-sided
## 32 AxcR2 / AverageFruitLength_cm r 0.0652052957 0.77729753 two-sided
## 33 AxcR1 / Fruit.large Homog. 0.0914789977 -0.46226195 less
## 34 AxcR2 / Fruit.large Homog. 0.1021589679 -0.36813505 less
## 35 AxcR1 / Fruit.small Homog. 0.8940530723 0.43263672 less
## 36 AxcR2 / Fruit.small Homog. 0.8968200109 0.42873919 less
## 37 AxcR1 / Consp.conspicuous Homog. 0.5144121459 -0.22763547 less
## 38 AxcR2 / Consp.conspicuous Homog. 0.5412733470 -0.08087569 less
## 39 AxcR1 / Consp.cryptic Homog. 0.4832004272 0.27520636 less
## 40 AxcR2 / Consp.cryptic Homog. 0.4511795915 0.09528052 less
## 41 AxcR1 / Endem.N Homog. 0.5800938861 1.29634665 less
## 42 AxcR2 / Endem.N Homog. 0.5403177585 -1.46739872 less
## 43 AxcR1 / Endem.Y Homog. 0.4143389765 1.32691247 less
## 44 AxcR2 / Endem.Y Homog. 0.4568520585 1.52039066 less
## Pvalue Pvalue.adj
## 1 1 1
## 2 1 1
## 3 0.464 0.729142857142857
## 4 0.585 0.745684210526316
## 5 0.464 0.729142857142857
## 6 0.585 0.745684210526316
## 7 1 1
## 8 1 1
## 9 0.234 0.792
## 10 0.295 0.920857142857143
## 11 0.51 0.920857142857143
## 12 0.442 0.920857142857143
## 13 0.666 1
## 14 0.713 1
## 15 0.933 1
## 16 0.942 1
## 17 0.045 0.528
## 18 0.601 0.745684210526316
## 19 0.983 1
## 20 0.985 1
## 21 0.141 0.504307692307692
## 22 0.591 0.745684210526316
## 23 0.586 0.920857142857143
## 24 0.382 0.920857142857143
## 25 0.876 1
## 26 0.331 0.920857142857143
## 27 0.834 0.873714285714286
## 28 0.196 0.792
## 29 0.771 1
## 30 0.798 1
## 31 0.759 1
## 32 0.489 0.920857142857143
## 33 0.442 0.920857142857143
## 34 0.496 0.920857142857143
## 35 0.563 0.920857142857143
## 36 0.552 0.920857142857143
## 37 0.423 0.920857142857143
## 38 0.43 0.920857142857143
## 39 0.584 0.920857142857143
## 40 0.57 0.920857142857143
## 41 0.895 0.895
## 42 0.153 0.748
## 43 0.818 1
## 44 0.858 1
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1RLQ axes and environmental variables
## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.juv, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 ELEV / AxcQ1 r 2.754935e-01 1.743928199 two-sided 0.066 0.231
## 2 DIST_TO_EDGE / AxcQ1 r -1.760315e-05 0.007077008 two-sided 0.993 0.993
## 3 CANOPY / AxcQ1 r -9.890480e-02 -1.549484414 two-sided 0.116 0.4212
## 4 TEN / AxcQ1 r -3.881277e-02 -0.655351763 two-sided 0.504 0.756
## 5 FIFTY / AxcQ1 r -3.845224e-02 -0.594885654 two-sided 0.379 0.7218
## 6 CECR / AxcQ1 r 2.706638e-02 0.474041392 two-sided 0.282 0.7218
## 7 UNDER.dense / AxcQ1 Homog. 1.502737e-01 -0.336376590 less 0.59 0.816923076923077
## 8 UNDER.low / AxcQ1 Homog. 2.036597e-01 -0.525871750 less 0.401 0.7218
## 9 UNDER.medium / AxcQ1 Homog. 6.171264e-01 1.702212261 less 0.963 0.974
## 10 ELEV / AxcQ2 r 1.925545e-02 0.133979858 two-sided 0.901 0.974
## 11 DIST_TO_EDGE / AxcQ2 r -1.362020e-01 -2.313959099 two-sided 0.021 0.231
## 12 CANOPY / AxcQ2 r -5.509804e-02 -1.037127674 two-sided 0.325 0.7218
## 13 TEN / AxcQ2 r 1.399334e-02 0.300300278 two-sided 0.742 0.954
## 14 FIFTY / AxcQ2 r 9.046060e-03 0.149636638 two-sided 0.851 0.957375
## 15 CECR / AxcQ2 r 4.142150e-02 0.847226853 two-sided 0.117 0.4212
## 16 UNDER.dense / AxcQ2 Homog. 3.018460e-01 2.340105936 less 0.991 0.993
## 17 UNDER.low / AxcQ2 Homog. 1.929088e-01 -0.974656749 less 0.064 0.384
## 18 UNDER.medium / AxcQ2 Homog. 5.010706e-01 -0.933944686 less 0.298 0.7218
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Fourth-corner Statistics
## ------------------------
## Permutation method Comb. 2 and 4 ( 999 permutations)
##
## Adjustment method for multiple comparisons: fdr
## call: fourthcorner.rlq(xtest = rlq.adu, nrepet = nrepet, modeltype = 6, typetest = "R.axes", p.adjust.method.G = "fdr", p.adjust.method.D = "fdr")
##
## ---
##
## Test Stat Obs Std.Obs Alter Pvalue Pvalue.adj
## 1 ELEV / AxcQ1 r 0.14022339 1.32154698 two-sided 0.202 0.434
## 2 DIST_TO_EDGE / AxcQ1 r 0.01288337 0.33631748 two-sided 0.779 0.842823529411765
## 3 CANOPY / AxcQ1 r 0.05280187 0.85151475 two-sided 0.434 0.646714285714286
## 4 TEN / AxcQ1 r 0.07951111 1.86534124 two-sided 0.045 0.3744
## 5 FIFTY / AxcQ1 r 0.04350150 1.15331139 two-sided 0.256 0.4608
## 6 CECR / AxcQ1 r -0.04232425 -1.14604755 two-sided 0.249 0.4608
## 7 UNDER.dense / AxcQ1 Homog. 0.17355089 -0.05312864 less 0.489 0.676285714285714
## 8 UNDER.low / AxcQ1 Homog. 0.28645051 1.92488001 less 0.965 0.965
## 9 UNDER.medium / AxcQ1 Homog. 0.53089374 -0.85525175 less 0.2 0.45
## 10 ELEV / AxcQ2 r 0.06836369 0.75587260 two-sided 0.476 0.646714285714286
## 11 DIST_TO_EDGE / AxcQ2 r -0.02305324 -0.64468775 two-sided 0.526 0.676285714285714
## 12 CANOPY / AxcQ2 r -0.08514258 -1.44000659 two-sided 0.168 0.432
## 13 TEN / AxcQ2 r -0.07075257 -1.66212636 two-sided 0.092 0.3744
## 14 FIFTY / AxcQ2 r -0.03532906 -1.01730191 two-sided 0.291 0.523636363636364
## 15 CECR / AxcQ2 r 0.05215427 2.00077290 two-sided 0.03 0.3744
## 16 UNDER.dense / AxcQ2 Homog. 0.18278557 0.22867378 less 0.601 0.68625
## 17 UNDER.low / AxcQ2 Homog. 0.23598540 -0.03940811 less 0.503 0.646714285714286
## 18 UNDER.medium / AxcQ2 Homog. 0.57870228 0.70731698 less 0.796 0.842823529411765
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Results can be represented using a table with colors indicating significance :
## [1] "juveniles"
## [1] "adults"
Significance with axes can also be reported on the factorial map of RLQ analysis. Here, significant associations with the first axis are represented in blue, with the second axis in orange, with both axes in green (variables with no significant association are in black)
## [1] "juveniles"
## [1] "adults"